1. Technical Field
The present invention relates to a Lamb-wave resonator using a Lamb wave and an oscillator including the Lamb-wave resonator.
2. Related Art
A Lamb wave is a plate wave, which is a bulk wave propagating inside a substrate by repeating reflections between upper and lower surfaces of the substrate when a thickness of the substrate is reduced to less than or equal to a few wavelengths of the wave to be propagated. Surface waves such as Rayleigh waves, leaky surface acoustic waves, and pseudo-longitudinal wave type leaky surface acoustic waves have 90% of energy within a depth of one wavelength from a surface of a substrate. However, unlike such surface waves, since the Lamb wave is a bulk wave propagating inside the substrate, its energy is distributed to a whole of the substrate. According to Choonpa Binran (Ultrasound Handbook), edited by Ultrasound Handbook Editorial Committee and issued by Maruzen Kabushiki Kaisha in 1999, pp. 62 to 71, plate waves and Rayleigh waves are scholarly distinguished. Further, in Acoustic wave element technical handbook, edited by the 150th committee of the Nippon Academy Promotion Association Acoustic Wave Element Technique and issued by Ohm-sha in 1991, pp. 148 to 158, a method for analyzing Rayleigh waves and leaky surface acoustic waves is described. Furthermore, Temperature characteristics of the substrate for lamb wave type elastic wave devices by Yasuhiko Nakagawa, Mitsuyoshi Shigeda, Kazumasa Shibata, and Shouji Kakio, IEICE Transactions on Electronics J-89C No. 1, pp. 34 to 39, a method for analyzing Lamb waves is described. As big differences between the waves, selection methods for a solution of an eighth equation are different, and Rayleigh waves and Lamb waves are completely different waves having different properties. Therefore, Lamb waves cannot provide favorable characteristics with same design conditions as those of Rayleigh waves. A design method specified for Lamb waves is thus required.
Further, as a characteristic of Lamb waves, similarly to a dispersion curve shown in JP-A-2003-258596, a mode that can propagate Lamb waves is a mode in which a wave number in a thickness direction of a substrate satisfies resonance conditions. Lamb waves have many modes including a high order. A phase velocity of existing modes of Lamb waves is larger than that of Rayleigh waves. Since many modes of them have a phase velocity that is larger or equal to that of “longitudinal wave”, a mode having a larger phase velocity can easily provide a high frequency even when a line width is the same as that of the surface wave described above. Further, an AT cut quartz substrate having a thickness of 5 wavelengths or less is employed, making it possible to use Lamb waves having an excellent temperature characteristic and being suitable for using a high frequency.
Furthermore, a Lamb-wave type high frequency resonator having an interdigital transducer (IDT) electrode including a first interdigital electrode and a second interdigital electrode that are interdigitated to each other on a main surface of a piezoelectric substrate and set to satisfy 21λ≦W≦54λ, where a cross width of the first interdigital electrode and the second interdigital electrode is W, and a wavelength of the Lamb wave is λ has been proposed (e.g. JP-A-2008-54163).
According to JP-A-2003-258596 described above, metal having a higher specific gravity is used as an electrode so as to increase a reflection coefficient of Lamb waves, thereby enabling energy trapping with less number of reflectors and achieving size reduction. This means that energy trapping is achieved by suppressing a vibration leakage in a lengthwise direction (a propagation direction of Lamb waves). However, it is hard to say that this electrode design is always optimum because energy trapping in a widthwise direction (a direction perpendicular to the propagation direction of Lamb waves) is not considered. Further, JP-A-2008-54163 does not disclose a specific method to increase energy trapping in the widthwise direction, either.
If a vibration leakage from an outer edge of a bus bar electrode toward a laterally outer edge of a piezoelectric substrate occurs, a spurious is caused by a reflection wave from the outer edge of the piezoelectric substrate.